4th International Conference on
Earthquake Geotechnical Engineering
June 25-28, 2007
Paper No. 1412
EFFECTS OF SOIL-STRUCTURE-EARTHQUAKE-INTERACTION ON
SEISMIC SOIL LIQUEFACTION TRIGGERING
Berna Unutmaz 1, K. Onder Cetin2
ABSTRACT
Although there exist some consensus regarding seismic soil liquefaction assessment of free field soil
sites, estimating the liquefaction triggering potential beneath building foundations still stays as a
controversial and difficult issue. Assessing liquefaction triggering potential under building foundations
requires the estimation of cyclic and static stress state of the soil medium. As part of these ongoing
studies, structural-induced shear stresses under building foundations subjected to cyclic loading are
attempted to be estimated. For this purpose, series of 3-D numerical simulations have been performed
on generic soil-structure sites. A new controlling parameter, β, was defined to assess the effects of
soil-structure-earthquake-interaction (SSEI) on liquefaction triggering. It is concluded that i) zones
extending 0.2 width inside and 0.8 width outside of the edges are found to be relatively more critical
from liquefaction triggering point of view as compared to the liquefaction potential of the zone in the
vicinity of the foundation centerline, ii) either positive or negative, effects of the presence of the
structure on liquefaction triggering potential of foundation soils diminishes rapidly at depths below 0.5
width and becomes almost none beyond the depths of 1.5 B, iii) the presence of the overlying structure
decreases liquefaction triggering potential for systems with a β value greater than 1.4. More
specifically, iv) for β values in the range of 0.5 to 1.0, due to the presence of the structure, CSR values
corresponding to the soil, structure and earthquake interacting system (i.e.: CSRSSEI) are estimated to
be twice as much the free field soil values at the ground surface, v) for the β values in the range of 1.5
to 2.0, CSRSSEI value is 25 to 40 % less than the free field values.
Keywords: soil-structure-earthquake interaction, cyclic stress ratio, liquefaction, sliding, rocking
INTRODUCTION
Evaluation of the in situ cyclic shear stress time history induced within any soil element (or stratum) is
a key component of any well-based method for assessment of the likelihood of “triggering”
seismically-induced soil liquefaction. The seismically-induced cyclic shear stress time history is, in
most analysis methods, normalized by some measure of the initial normal effective stress in the soil, to
give rise to the earthquake-induced cyclic shear stress ratio (CSR). At most soil sites, the cyclic shear
stresses acting on horizontal planes due to seismic loading are largely dominated by cyclic shear
stresses induced by vertically propagating, or nearly vertically propagating, shear waves. This gives
rise to the "simplified" procedure for evaluation of induced cyclic shear stresses at depth (Seed and
Idriss, 1971). When this “equivalent uniform cyclic shear stress” is normalized by the initial effective
overburden stress, the result is an estimate of the “equivalent uniform cyclic stress ratio” (CSR) as:
a
γ⋅h
CSR = 0.65 ⋅ max ⋅
⋅ rd
(1)
g
σ′v
1
Graduate Student Researcher, Department of Civil Engineering, Middle East Technical University,
Ankara, Turkey, Email: bunutmaz@metu.edu.tr
2
Assoc. Prof. Dr, Department of Civil Engineering, Middle East Technical University, Ankara,
Turkey
The stress reduction coefficient, rd, is a function of site stratigraphy, soil properties, and characteristics
of the "input" motions (excitations). It has a value of 1.0 by definition at the ground surface. Cyclic
stress ratio; CSR was chosen as demand term for liquefaction triggering assessment of Seed et al
(1984). Since then, numerous researchers, still adopting CSR as the demand term (Liao et al., 1988,
Liao and Lum, 1998, Youd and Noble, 1997, Toprak et al., 1999, Juang et al, 2002, Cetin et al., 2004)
have attempted to improve the accuracy of liquefaction triggering relationships. However, all these
methods founded on “simplified procedure” suffer from a major limitation that they are all applicable
to the liquefaction triggering assessment of free field soil sites. Direct applicability of these methods to
foundation soils underlying structural systems is not possible, unless, in the estimation of CSR,
structure-soil-earthquake interaction is properly addressed. More specifically, compared to a free field
soil site, under static conditions, due to the presence of an overlying structural system i) overburden
stresses acting on the underlying foundation soils are higher, ii) nonzero shear stresses act on the
horizontal soil planes. Similarly during earthquake shaking, presence of iii) foundation elements (e.g.:
footings or mat) forms usually a sharp impedance contrast which causes deviations from the free field
vertical propagation pattern of shear waves (i.e. : kinematic interaction), iv) an overlying structure due
its inertia will exert additional cyclic shear stresses on to foundation soils. Issues referred to in (i) and
(ii) can be handled by introducing series of correction factors formerly known as Kα, and Kσ,
respectively applied on CSReq as given in Equation (2).
CSReq ,α = 0,σ V ' =100 kPa =
CSReq ,α ,σ v '
(2)
Kα ⋅ Kσ
Kα factors as a function of relative density, DR, and α as defined in Equation (3) were introduced by
Seed (1983) to assess the effects of initial static shear stresses on liquefaction triggering resistance.
Since then number of researchers have studied this issue and have shown that Kα is mainly dependent
on soil stiffness and confining stress conditions. A review of the literature was presented by Harder
and Boulanger (1997) as part of NCEER 1997. More recently, Boulanger (2003, 1) proposed a new set
of Kα corrections as a function of relative dilatancy index (ξR). Based upon currently available Kα
corrections, it can be concluded that from only Kα point of view, due to the presence of an overlying
structure, decrease in liquefaction triggering resistance of loose foundation soils is expected especially
near the foundation edges. Figure 1 presents a typical α and Figure 2 shows Kα fields developed
along the center line of a 4 story residential structure founded on a mat underlain by a sand layer with
relative densities of 30 % and 70 %, respectively. As can be interpreted from Figure 2, Kα effects
increase seismic demand (i.e. CSR) for “loose” soils.
0.75
0.50
0.25
0.00
InitialStatic Shear Stress τstatic, horizontal
=
Vertical Effective Stress
σv '
(3)
Edge of the
building
y
x
L
α
α=
B
0.0
0.2
0.4
0.6
x/B
0.8
1.0
1.2
1.4
1.6
z
1.8
Figure 1. Variation of “α” along the width of the structure at z/B = 0 and y/L = 0
2.00
2.00
Kα
Kα
1.00
0.00
1.00
0.00
0.0
0.2
0.4
0.6 0.8
x/B
(a)
1.0
1.2
1.4
1.6
1.8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
x/B
(b)
Figure 2. Kα along the width of the structure, for (a)DR = 30%, (b) DR = 70% z/B = 0 and y/L = 0
The additional effect of reduction of normalized liquefaction resistance with increased initial effective
overburden stress ( σ v′ ) has been demonstrated by means of laboratory testing, and is a manifestation
of “critical state” type of behavior (suppression of dilatancy at increased effective confining stress). Kσ
concept has been addressed by a number of researchers (e.g.: NCEER Working Group, Youd et al.,
2001; Boulanger, 2003 (2). Cetin et al. (2004); Idriss and Boulanger, 2006). Equation (4) presents the
recommendations of Cetin et al. (2004) regarding the correction factor Kσ.
⎛ − 3.2 ⋅ ln (σ v ' Pa ) ⎞
K σ = exp⎜
⎟
13.32
⎝
⎠
(4)
As evident by the available literature, even though there exist some disagreements on the actual values
of Kα, and Kσ factors, yet it is still possible to compare the free field soil CSR (i.e.: CSRFF ) values to
the CSR value estimated for a soil, structure and earthquake interacting system (i.e.: CSRSSEI) through
currently available Kα, and Kσ correction factors, if both kinematic and inertial interaction components
are put aside.
The kinematic and inertial interactions defined in iii) and iv) are rather complex and deserve further
attention on the soil structure and earthquake interaction (SSEI) problem from liquefaction triggering
point of view. Veletsos and Meek (1974) discovered that a) σ (ratio of structure-to-soil stiffness) as
defined in Equation (5), b) the ratio of structure height to foundation radius (width) and c) the
interaction of the fixed-base natural frequency of the structure to the frequency regions of the design
spectrum were the critical factors controlling SSEI. By Veletsos and Meek, it was concluded that for σ
values in the range of 3-20, soil-structure interaction becomes critical.
σ=
Vs ,final × Tstr
h effective
(5)
Yoshimi and Tokimatsu (1977) have shown that as the width ratio, (B/D) of a structural system
increases, the settlement ratio, (S/D) decreases. Finn and M. Yodengrakumar (1987) have performed
centrifuge model tests as well as finite element simulations and revealed that seismically-induced pore
pressure generation in foundation soils especially near the external wedges was faster than the one in
the free field. Rollins and Seed (1990) based on a number of shaking table and centrifuge model tests,
concluded that usually pore pressure generation was slower beneath the buildings than the one in the
free field. They have also concluded that if spectral acceleration ratio, Sa/amax was larger than about
2.40, the induced cyclic stress ratio value would be higher beneath the building than the one in free
field. Popescu and Prevost (1993) have performed centrifuge model tests and numerical simulations;
however, lack of pore pressure transducers installed at the edges of the model structure during
centrifuge tests disabled them quantifying the interaction effects on pore pressure generation. Jun-Tsai
Hwang et al. (1994) have conducted a two dimensional effective stress based analysis of soil-structureearthquake interaction and concluded that the soils outside the structural influence zone liquefy first,
followed by the zone under the structure. Yoshiaki et al. (1997) have performed shaking table tests,
using sand box with a footing model, along with numerical simulation of the test setup. They have
concluded that, soils directly beneath the footing would be harder to liquefy than free field soils,
whereas the region near the external wedge of footing was more susceptible to liquefaction than the
free field soil region. Similarly, Liu and Dobry (1997) have performed shaking table tests with sand
box containing model footings, and suggested that a weak zone of liquefaction resistance locating
around the line starting from the external end point of footing base and inclining 45° to the horizontal
direction exists. Stewart et al. (1999) presented a summary of the existing literature on soil structure
interaction problems and described analysis procedures and system identification techniques for
evaluating inertial soil structure interaction effects on seismic structural response. Two sets of
analyses, aiming to estimate period lengthening ratio and foundation damping factors, as well as soil
structure system identification procedures were presented for the evaluation of vibration parameters.
More recently, Travasarou et al. (2006) have performed 2-D soil-structure interaction analyses for two
representative buildings in Adapazari, Turkey and showed that for stiff structures on shallow
foundations, seismic demand was considerably higher than free field adjacent to the perimeter of the
structure and conversely for typical static building loads, the demand was reduced by 50% directly
underneath the foundation of the structure.
As clearly presented by the summarized literature, there exist contradicting arguments regarding the
effects and the assessment of liquefaction triggering potential of foundation soils overlain by structural
systems. Within the confines of this paper, it is attempted to present the preliminary results of our
ongoing research studies aiming to comparatively quantify the effects of SSEI on liquefaction
triggering potential, more specifically on CSR. The scope of our studies includes 3-D numerical
simulation of SSEI.
NUMERICAL SIMULATIONS
3-D finite difference-based simulations were performed for the purpose of assessing SSEI. For
verification purposes additional 1-D soil site response analyses were performed by SHAKE91
software. The numerical assessment scheme included the followings : i) 3-D static assessment of soilstructure system for the purpose of estimating horizontal shear stresses and vertical effective stresses,
which will be further used in the calculation of Kα and Kσ correction factors ii) 3-D seismic
assessment of soil-structure system for the purpose of estimating both structural and soil mass-induced
shear stresses acting on the horizontal plane, which will be further used in the calculation of CSR, iii)
3-D seismic assessment of the free field soil site (without the structural system) for the purpose of
enabling direct comparisons with 1-D SHAKE 91 simulations, useful for the calibration of the 3-D
model. In the development of the 3-D finite difference mesh, mesh window and element sizes were
selected in such a way that the results of FLAC 3-D free field simulations match with SHAKE 91
results, as illustrated in Figure 3, Figure 4 and Figure 5.
0
τ max (kPa)
10
0.0
20
0
0
5
5
0.2
a max (g)
0.4 0.6
0.8
0.50
FLA C 3D,
Free Field
Depth (m)
Depth (m)
15
20
15
20
FLA C 3D,
Free Field
25
30
SHA KE 91
30
Figure 3. Variation of shear
stress (τ) with depth (d)
0.30
5% Damping
0.20
0.10
0.00
25
35
S A (g)
10
10
SHAKE91
FLAC 3D, Free Field
0.40
SHA KE 91
0.0
1.0
2.0
Period (se c)
3.0
4.0
35
Figure 4. Variation of
amax with depth (d)
Figure 5. Comparison of elastic
response spectra
Figure 6 presents a typical mesh adopted for the numerical simulations. In FLAC 3-D simulations, to
be consistent with the available liquefaction triggering methods (e.g.: NCEER, 1997, Cetin et al. 2004)
equivalent linear model with hysteretic degradation and damping curves as recommended by Vucetic
and Dobry (1991) for clean sands (i.e.: PI = 0) was adopted for the purpose of estimating induced
shear stresses. The spatial element size is selected to be smaller than approximately one-tenth of the
wavelength associated with the highest frequency component of the input wave, which is 15 Hz, to
prevent numerical distortion of the propagating wave in dynamic analyses. The boundary condition at
the sides of the model is selected as free field which accounts for the free field motion that would exist
in the absence of the structure.
Figure 6. Finite Difference 3D Mesh
As shown in Figure 7, four generic 30 m thick homogeneous soil profiles with shear wave velocity
values selected as Vs=100 m/sec, Vs=150 m/sec, Vs=200 m/sec and Vs=300 m/sec, overlain by two
different structural systems with fixed base natural periods of 0.38 and 0.22 seconds are shaken by
1999 Kocaeli Earthquake, Mw = 7.4, Sakarya (SKR) record, 1989 Loma Prieta Earthquake, Mw = 7.0
Santa Cruz USCS Lick Observatory Station (LP) record and 1995 Kobe Earthquake, Mw = 6.9,
Chihaya Station (CHY) record. Foundation systems are defined as 30 cm thick surfacial mats, overlain
by a regular concrete column-beam system with column and beam dimensions of 40 x 40 and 30 x 30
cm, respectively. Column spacing and storey heights were selected as 4 and 3 m respectively. The
storey masses were concentrated at the floor levels.
Tstr=0.22 sec
Tstr=0.38 sec
8m
8m
Clean Sand
Vs = 150 m/sec
G = 40,500 MPa
K = 88,000 MPa
γ = 18 kN/m3
Clean Sand
Vs = 100 m/sec
G = 18,000 MPa
K = 39,000 MPa
γ = 18 kN/m3
(g)
0.40
8m
8m
Clean Sand
Vs = 300 m/sec
G= 162,000 MPa
K=8.0x106 MPa
γ = 18 kN/m3
Clean Sand
Vs = 200 m/sec
G = 72,000 MPa
K=3.5x106 MPa
γ = 18 kN/m3
0.30
0.20
0.10
0.00
-0.10
0
20
40
60
80
100
-0.20 1.00
-0.30
-0.40
0.80
0.60
0.40
1999 Kocaeli EQ
(SKR)
2.0
3.0
200
300
400
2.00
0.50
1.60
0.40
0.80
0.40
1.0
100
1.20
0.20
0.00
0.0
0
4.0
0.00
0.0
0
10
20
30
40
50
0.30
1989 Loma Prieta EQ
(LP)
1.0
2.0
3.0
4.0
0.20
0.10
0.00
0.0
1995 Kobe EQ
(CHY)
1.0
2.0
3.0
4.0
Figure 7. Schematic view of soil-structure and earthquake combinations
As presented in Table 1, 19 sets of numerical simulations were performed corresponding to different
combinations of generic soil sites, structures and earthquake records. As shown in Figure 8, the results
of these simulations are presented in the form of corrected CSR values. As shown in Equation (6), in
estimating the CSR values of the soil-structure-earthquake interacting model, initial static horizontal
shear stresses, τ static,h , were subtracted from the estimated maximum horizontal cyclic shear stresses,
τ SSEI ,h , further normalized by static vertical effective stresses leading to CSRSSEI values. CSRSSEI was
then corrected by Kα and Kσ factors to eliminate the variabilities due to initial static vertical effective
and horizontal shear stresses.
0.65 ⋅ (τ SSEI ,h − τ static ,h )
CSR SSEI ,α =0,σ v '=100 kPa =
σ v ' ,static
(6)
Kα ⋅ Kσ
The maximum cyclic shear stresses developed within the free field soil medium (simulated by using
the exact same numerical model, but without the structure) were normalized by static vertical effective
stress, and the free field CSR values (CSRFF) were estimated. These values were also corrected by Kσ
factors but not Kα factors due to lack of horizontal shear stresses in free field level soil sites. Then the
ratio of CSRSSEI to CSRFF was defined as CSRR, a direct measure of the kinematic and inertial
interaction of the soil, structure and earthquake.
Table 1. Input and Output Parameters of Numerical Simulations
Vs,initial
Vs,final
Tstr
(m/sec)
(m/sec)
(sec)
100
100
150
150
200
200
300
300
100
100
150
150
200
200
100
150
150
200
200
60
60
103
103
149
149
235
235
62
62
97
97
136
136
79
122
122
163
163
0.38
0.22
0.38
0.22
0.38
0.22
0.38
0.22
0.22
0.38
0.22
0.38
0.22
0.38
0.38
0.22
0.38
0.22
0.38
CSRRpeak,z/B=0
EQ
PGA SA at
SA/PGA
(g) T=Tstr
2.41
2.44
1.64
2.36
1.18
1.50
0.42
0.61
2.33
1.78
2.05
0.70
2.31
0.39
2.34
0.77
0.73
0.53
0.47
SKR
SKR
SKR
SKR
SKR
SKR
SKR
SKR
LP
LP
LP
LP
LP
LP
CHY
CHY
CHY
CHY
CHY
0.15
0.15
0.18
0.18
0.26
0.26
0.36
0.36
0.11
0.11
0.15
0.15
0.23
0.23
0.05
0.08
0.08
0.12
0.12
0.22
0.41
0.38
0.38
0.54
0.42
0.68
0.81
0.30
0.39
0.43
0.53
0.56
0.66
0.14
0.40
0.35
0.54
0.22
1.45
2.78
2.15
2.14
2.10
1.61
1.87
2.25
2.77
3.63
2.82
3.45
2.39
2.84
2.61
5.00
4.38
4.44
1.81
σ
Tsoil
2.87
1.66
4.93
2.85
7.11
4.10
11.21
6.47
1.71
2.97
2.68
4.64
3.74
6.47
3.76
3.37
5.83
4.49
7.77
1.20
1.20
0.80
0.80
0.60
0.60
0.40
0.40
1.20
1.20
0.80
0.80
0.60
0.60
1.20
0.80
0.80
0.60
0.60
Tstr/Tsoil Tsoil/Tp
0.32
0.18
0.48
0.28
0.64
0.37
0.95
0.55
0.18
0.32
0.28
0.48
0.37
0.64
0.32
0.28
0.48
0.37
0.64
4.62
4.62
3.08
3.08
2.31
2.31
1.54
1.54
7.50
7.50
5.00
5.00
3.75
3.75
5.45
3.64
3.64
2.73
2.73
β
0.46
0.51
1.02
0.59
1.33
0.59
1.78
1.24
0.51
1.15
0.78
1.64
0.88
1.80
0.83
1.38
2.09
1.63
1.15
Figure 8 present the variation of CSRR with depth and parallel to the width of the structure across the
centerline of the structure. Depending on the soil, structure and earthquake characteristics, CSRSSEI
was estimated to be higher or lower than the CSRFF values.
3.0
2.0
1.0
0.0
0.1
0.0
2.0
1.0
0.0
0.1
0.0
2.0
1.0
0.0
0.1
0.0
2.0
1.0
0.0
0.1
0.0
0.0 0.2 0.4
0.6 0.8 1.0 1.2
x/B
1.4 1.6 1.8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
x/B
(a)
(b)
(c)
Figure 8. Variation of (a) CSRSSEI and CSRFF (b) and (c) CSRR through Depth
The variation of CSRR along the distance parallel to the structure width follows two patterns as also
illustrated in Figure 9 (a) and (b). For case (b), it is concluded that SSEI is beneficial and reduces the
seismic liquefaction triggering demand from the nearby foundation soils and opposite is true for case
(a).
3.0
CSRR
2.5
2.0
CSRRpeak
1.5
(a)
1.0
0.5
(b)
CSRRpeak
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
x/B
Figure 9. Schematic representation of CSRRpeak
DISCUSSION ON NUMERICAL SIMULATIONS RESULTS
The analyses results were summarized in Figure 10 in the form of variation of CSRR with normalized
depth (i.e.: depth/width of structure; z/B) and distance along the centerline of the building (x/B). As
can be interpreted from the results provided, SSEI effects on seismic soil liquefaction triggering can
not be concluded to be consistently beneficial or detrimental. Usually under the structure (i.e.: x/B <
0.5), CSRR is less than 1.0, stating that generally under buildings, SSEI effects reduce the seismic soil
liquefaction triggering demand from the foundation soils. However, starting with the edges of the
structure to a distance of 1.5B from the center of the building, CSRR values are higher than 1.0 (i.e.:
CSRSSEI > CSRFF), which states that presence of the overlying structure negatively affects the soils in
1B neighborhood of the structure. As illustrated by Figure 11, SSEI effects, either positive or negative
become less significant beyond a z/B ratio of 1. (i.e. CSRSSEI approaches to the value of CSRFF).
CL
Depth
0m
3.0
z/B=0.0625
2.0
1.0
0.0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
3.0
2.0
z/B=0.1875
1.0
0.0
3.0
z/B=0.3125
2.0
1.0
0.0
30 m
Figure 10. All CSRR values for z/B=0.0625, z/B=0.1875 and z/B=0.3125
0.0
1.0
2.0
3.0
0.0
0.2
0.4
0.6
z/B
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Figure 11. Variation of CSRRpeak with depth along centerline
To quantify the effects of SSEI, CSRRpeak values at the foundation levels were drawn against the SSI
parameter of σ (Veletsos and Meek), SA (Seed and Rollins). As presented in Figure 12, the
correlation between CSRRpeak vs SA was found to be weak. The R2 terms are calculated as 0.63 and
0.22, for σ and SA parameters respectively.
3.00
3.00
R 2 = 0.63
R 2 = 0.22
2.50
2.00
CSRR peak,z/B =0
CSRR peak,z/B =0
2.50
1.50
1.00
2.00
1.50
1.00
0.50
0.50
0.00
0.00
0
2
4
σ
6
8
10
0.0
12
0.5
SA
1.0
Figure 12. CSRRpeak,z/B=0 vs. σ and SA
Inspired by these, a new term, “β”, that will model the interaction among soil, structure and
earthquake is introduced, as given in Equation (7), where Tstr is the fixed base period of the structure,
Tsoil is the pre-earthquake period of the soil which is found by (8), SA is the spectral acceleration value
corresponding to the fixed base period of the structure, and PGA is the peak ground acceleration of the
free field soil site. For the ease of use, pre-earthquake periods of the structure and soil are taken into
account in this new term “β”. As shown in Figure 13, the correlation between CSRRpeak,z/B=0 vs. this
new term, β, is found to be stronger, as evidenced by an R2 of 0.75.
β=
Tstr S A
⋅
Tsoil PGA
(7)
4 H soil
Vs , initial
(8)
Tsoil =
3.00
3.00
CSRRpeak = -1.46Ln( β ) + 1.48
R2 = 0.75
2.50
2.50
LP
SKR
R2 = 0.90
R2 = 0.82
2.00
CSRR peak,z/B=0
CSRR peak,z/B=0
2.00
1.50
1.00
0.50
CHY
1.50
1.00
0.50
R2 = 0.50
0.00
0.00
0.0
0.5
1.0
β
1.5
2.0
2.5
0.0
Figure 13. CSRRpeak,z/B=0 vs. β
0.5
1.0
β
1.5
2.0
2.5
For practical purposes, CSRRpeak,z/B=0 can be estimated as given in Equation (9). Based upon Equation
(9), it is concluded that the presence of the overlying structure decreases liquefaction triggering
potential for systems with a β value of greater than 1.4. For β values in the range of 0.5 to 1.0, due to
the presence of the structure, CSR values corresponding to the soil, structure and earthquake
interacting system (i.e.: CSRSSEI) are estimated to be twice as much the free field soil values at the
ground surface. Similarly, it can be concluded that for the β values in the range of 1.5 to 2.0, CSRSSEI
value is 25 to 40 % less than the free field values.
CSRR peak ,z / B=0 = −1.46 ln β + 1.48
(9)
SUMMARY AND CONCLUSIONS
Within the confines of this paper, a review on seismic soil structure interaction problem, emphasis on
its effects to seismic soil liquefaction triggering, is presented. Motivated by lack of available models
for the purpose of assessing liquefaction triggering potential of soils overlain by a structure, it is
intended to develop an empirically-based relationship to estimate CSR values of such soil structure,
earthquake interacting system as compared to the values of a free field soil site. Thus, series of 3-D
numerical simulations of generic soil, structure systems shaken by three earthquake records were
performed. The results were summarized in the form of Kα, Kσ corrected CSR values. Then the ratio
of the CSR values estimated for the SSEI system and free field soil site was defined as CSRR. A new
soil, structure, earthquake interaction parameter β, was defined to assess the independency of CSRR. It
was concluded that the proposed parameter, β can capture the effects of SSEI on liquefaction
triggering well as evident by a high R2 value of 0.75. Based upon analyses results following
conclusions were made:
i)
ii)
iii)
Zone extending 0.2 width inside and 0.8 width outside of the edges are found to be
relatively more critical from liquefaction triggering point of view as compared to the
liquefaction potential of the zone in the vicinity of the foundation centerline.
Either positive or negative, effects of the presence of the structure on liquefaction
triggering potential of foundation soils diminishes rapidly at depths below 0.5 width and
becomes almost none beyond the depths of 1.5 B.
The presence of the overlying structure decreases liquefaction triggering potential for
systems with a β value greater than 1.4.
More specifically,
iv)
v)
For β values in the range of 0.5 to 1.0, due to the presence of the structure, CSR values
corresponding to the soil, structure and earthquake interacting system (i.e.: CSRSSEI) are
estimated to be twice as much the free field soil values at the ground surface.
For the β values in the range of 1.5 to 2.0, CSRSSEI value is 25 to 40 % less than the free
field values.
As the concluding remark, we would like to clarify our intention. All these preliminary findings were
based on limited number of numerical simulations as part of our ongoing research studies. More
simulations are going to be performed with i) natural soil profiles as opposed to generic soil sites, ii)
structures of larger natural periods in the range of 0.4 to 1.0 seconds with and without basements, iii) a
suite of earthquake records sampled from near-field, mid-field and far-field motions where our current
database has a gap. After these, we believe that the resulting model will be more general and powerful.
However, even these limited simulation results revealed that the proposed controlling parameter, β for
the assessment of liquefaction triggering potential of foundation soils is promising.
ABBREVIATIONS
α
Ratio of static shear stresses to effective vertical stress
β
Soil-structure-earthquake interaction factor
CSR
Cyclic stress ratio
Equivalent cyclic stress ratio
CSReq
CSR for free field soil sites
CSRFF
CSR for soil-structure-earthquake interaction
CSRSSEI
CSRR
Ratio of structure CSR to free field CSR
CSRRpeak Maximum/minimum CSRR beneath the foundation
CSRR along midline of the structure
CSRR0
heffective Effective height of structure (generally taken as two thirds of the total height)
Correction factor for static shear stresses
Kα
Correction factor for overburden
Kσ
σ
Ratio of structure to soil stiffness
PGA
Peak ground acceleration
Spectral acceleration at the period corresponding to Tstr
SA
Pa
Atmospheric pressure
Fixed base natural period of the structure
Tstr
Predominant period of earthquake
TP
Period of soil site
Tsoil
Initial shear wave velocity of the site
Vs,initial
Final shear wave velocity of the site
Vs,final
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